It is not an issue, in fact that's exactly how the entry should be completed. Even though one employer sends multiple W2 copies to accommodate the local, and sometimes state withholding if there is more than one state, you enter it as though it is one W2.
In your case the second W2 has only local information on it, so when you review your W2 entry make sure you only entered one W2 and include the local tax from your 2nd W2 on the one W2 entry in TurboTax.
Kentucky (KY) and Ohio (OH) have a reciprocal agreement which means you file all of your income on your resident state return. If sounds like your employer withheld only KY state tax in which case nothing needs to be completed for OH.
The local tax would have no bearing on your federal or state return results. Double check your W2 entries (click the image attached to enlarge and view). Delete a second W2 if you entered one.